This note is focused on a noveltechnique to establishthe boundedness in more regular spacesfor global attractorsof dissipative dynamical systems,without appealing to uniform-in-timeestimates.As an application,we consider the semigroupgenerated by thestrongly damped wave equationwith critical nonlinearity,whose attractor is shown to possessthe optimal regularity.
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Conti et al. (2009) studied this question.
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